Answer: (a) α = 
(b) For r≤R: B(r) = μ_0.
For r≥R: B(r) = μ_0.
Explanation:
(a) The current I enclosed in a straight wire with current density not constant is calculated by:
where:
dA is the cross section.
In this case, a circular cross section of radius R, so it translates as:
For these circunstances, α =
(b) <u>Ampere's</u> <u>Law</u> to calculate magnetic field B is given by:
μ_0.
(i) First, first find for r ≤ R:
Calculating B(r), using Ampere's Law:
μ_0.
.μ_0
B(r) = 
.μ_0
B(r) = 
.μ_0
For r ≤ R, magnetic field is B(r) = .μ_0
(ii) For r ≥ R:
So, as calculated before:
I
Using Ampere:
B.2.π.r = μ_0.I
B(r) = 
.μ_0
For r ≥ R, magnetic field is; B(r) = .μ_0.
Answer: M = 6.13 × 10^18 kg
Explanation:
g = GM/r2,
Where
The mass M of the asteroid = ?
The radius r = 110000 m
g = 0.0338 m/s^2
G is the gravitational constant.
SI units its value is approximately 6.674×10^−11m3⋅kg−1⋅s−2
Using the formula
g = GM/r2
Cross multiply
GM = gr^2
6.674×10^-11M = 0.0338 × 110000^2
M = 408×10^6/6.674×10^-11
M = 6.13 × 10^18 kg
Momentum = (mass) x (speed)
Mass is constant, so the rate of change of momentum is
(mass) x (rate of change of speed) .
But (rate of change of speed ) is just acceleration.
So the rate of change of momentum is (mass) x (acceleration).
But (mass) x (acceleration) is Force.
So Force is the rate of change of momentum. Verrrrrrrry interesting !
In this problem, Force = (40 kg) x (9 m/s²) = 360 newtons.
One 'Newton' is one kilogram-meter per second² .
Unit of momentum is (kilogram)-(meter per second), so 'newton'
is also a unit of time rate of change of momentum.
Rate of change of momentum is 360 momentum units per second.
Answer:
Explanation:
Kinetic energy of ball in motion = 1/2 m v² . Potential energy = 0
Let the minimum distance between the balls be d on collision.
Electric potential energy at that time= k Q²/d , Here kinetic energy is converted into potential energy . So
1/2 m v² = kQ²/d
d =2 k Q² / mv²,= 18 x 10⁹ x Q²/ m v².
